Governing equations - Navier-Stokes
Growth rate \(\Psi(x, z, t) = Ae^{-\alpha|z|}\exp\left[i\alpha(x-ct)\right]\)
Assumptions - fluid behaviour of 2 layers with a perturbed interface, etc. Applies equally to layers of gases, liquids, or viscous solids.
Basic scalings - density contrast and wavelength per unit thickness
Review papers that have applied these equations to the lithosphere (e.g., \citealp*{Conrad1997}).
Result - drips are expected to be 100 km in wavelength, but could be larger if background strain rate (shortening) is high
Limitations (which leads into models) - boundary conditions, complicated rheologies

Other modes of foundering

Foundering of a dense root: It's similar to RTI but doesn't fit the simple scheme above. Instead of 2 layers with an interface, there is a third body imposed within or between the layers.
Weakening by fluids or melt and breaking off? (Northern Andean volcanic zone)
Ablative removal, thermal erosion, shear entrainment, subduction removal, ... ?

Models - keep it brief

Scale of RTI should be ~100 km, larger if b/g strain rate is high
Scale of other modes: smaller for weakened foundering, larger for root removal?
Time scales?
Volcanism and sources of melt - melting of drips possible
Can we distinguish between RTI, weakened foundering, and root removal? If so, that would be a major part of the rest of the paper.